The author proves several 1997 Borwein-Bradley-Broadhurst conjectures and general reduction formulas for alternating multiple zeta values using iterated integrals.
Multiple zeta-star values and multiple integrals
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abstract
We prove a kind of integral expressions for finite multiple harmonic sums and multiple zeta-star values. Moreover, we introduce a class of multiple integrals, associated with some combinatorial data (called 2-labeled posets). This class includes both multiple zeta and zeta-star values of Euler-Zagier type, and also several other types of multiple zeta values. We show that these integrals can be used to obtain some relations among such zeta values quite transparently.
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math.NT 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Evaluations of multiple polylogarithm functions, multiple zeta values and related zeta values
The author proves several 1997 Borwein-Bradley-Broadhurst conjectures and general reduction formulas for alternating multiple zeta values using iterated integrals.